The confined system approximation for solving non-separable potentials in three dimensions


JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, vol.31, no.13, pp.3095-3114, 1998 (SCI-Expanded) identifier identifier


The Hilbert space L-2(R-3), to which the wavefunction of the three-dimensional Schrodinger equation belongs, has been replaced by L-2(Omega), where Omega is a bounded region. The energy spectrum of the usual unbounded system is then determined by showing that the Dirichlet and Neumann problems in L-2(Omega) generate upper and lower bounds, respectively, to the eigenvalues required. Highly accurate numerical results for the quartic and sextic oscillators are presented for a wide range of the coupling constants.